Block #1,454,426

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2016, 1:04:33 PM · Difficulty 10.7207 · 5,362,785 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

6fbdd1c3463448248dd8477d573c4731c4110cf130b3d85c543cba558b1b97db

View on Chainz ↗

Height

#1,454,426

Difficulty

10.720744

Transactions

Size

936 B

Version

Bits

0ab882ac

Nonce

1,571,621,096

Timestamp

2/13/2016, 1:04:33 PM

Confirmations

5,362,785

Mined by

⛏️ P2SHAHe52Z3NKhhwStFdg6fAdi4fJSPKhzZedV

Merkle Root

43862ca8fd164bbf5172cc5fcea984f8b97de7a14b378dfa4366a0cfd11b9a33

Transactions (2)

Coinbase3ca27a4d6ac25b…6a7e99167a50cb

1 in → 1 out8.7000 XPM110 B

AHe52Z3N…PKhzZedV

dc907666761898…b94f552a33bf86

1 in → 17 out61.2572 XPM736 B

AVA234pf…hfXcvGVm ARbmELZZ…D2EmA9eK AeXAXtpC…BHw75LdP AQHFP8XD…t5oMNd7N AS7EhQy8…svFmz7yp

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.809 × 10⁹⁵(96-digit number)

28096789219608921993…39021546138710890559

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.809 × 10⁹⁵(96-digit number)

28096789219608921993…39021546138710890559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.809 × 10⁹⁵(96-digit number)

28096789219608921993…39021546138710890561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.619 × 10⁹⁵(96-digit number)

56193578439217843987…78043092277421781119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.619 × 10⁹⁵(96-digit number)

56193578439217843987…78043092277421781121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.123 × 10⁹⁶(97-digit number)

11238715687843568797…56086184554843562239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.123 × 10⁹⁶(97-digit number)

11238715687843568797…56086184554843562241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.247 × 10⁹⁶(97-digit number)

22477431375687137594…12172369109687124479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.247 × 10⁹⁶(97-digit number)

22477431375687137594…12172369109687124481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.495 × 10⁹⁶(97-digit number)

44954862751374275189…24344738219374248959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.495 × 10⁹⁶(97-digit number)

44954862751374275189…24344738219374248961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,454,426

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